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Algebra I Practice Test
Inequalities and Absolute Value
Name
Date
Unit 3
Period
Vocabulary: Define each word and give an example.
1.
Less Than
2.
Absolute Value Equation
3.
Compound Inequality
Short Answer:
4.
Solving a linear inequality is similar to solving linear equations with what one exception?
5.
Describe and give an example of the difference between a compound inequality that is an “or” statement and a
compound inequality that is an “and” statement.
6.
Explain why an absolute value equation can have two solutions. Illustrate with an example.
Review:
7.
Find the first and third quartiles and interquartile range for the following set of data: 2, 5, 5, 8, 10, 15, 20, 22, 25
Q1 =
Q3 =
IQR =
8.
Name the property illustrated by a ( b + c ) = ab + ac .
9.
Solve the equation. 8 p ­ 8 = 2 ( 5 ­ 2 p ) + 10
10. For Vera’s cellular phone service, she pays $32 a month, plus $0.75 for each minute over the allowed
minutes in her plan. Vera received a bill for $47 last month. For how many minutes did she use her phone
beyond the allowed minutes?
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Algebra I Practice Test
Inequalities and Absolute Value
Unit 3
Problems:
**Be sure to show all work used to obtain your answer. Circle or box in the final answer.**
11. Solve the linear inequality and graph the solution on a number line.
a.
3
d  6
4
b.
c.
4t  2  14
d.
4  2  a
x  3  2( x  1)
12. Lorene’s employer pays her $8.50 per hour plus an additional $45 per week. Lorene would like to earn enough
money to purchase a stereo system that costs $300. Write and solve an inequality that represents the number of
hours, h, that Lorene can work this week in order to be able to purchase the stereo. 13. Write an inequality for each verbal statement.
a.
Karen has $3 to spend in the arcade. The game she likes costs $0.50 to play. What are the possible number
of times that she can play? (Let p represent the # of games she can play.)
b.
The minimum score to stay in the game is 80. (Let m represent the minimum score.)
14. Write a compound inequality for each number line shown below.
a.
b.
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Algebra I Practice Test
Inequalities and Absolute Value
Unit 3
15. Solve the compound inequality and graph the solution on the number line.
a.
6  2 x  20 or 8  x  0
b.
8  2 y  6  18
c.
4 x  7  x  8 or  31  2 x  11
d.
13  5  2 x  9
16. Solve the absolute value equations.
a.
6 x
b.
2 w  5  13
c.
6  3x  1  8
d.
3 x  1  5  13
17. Solve the absolute value inequalities and graph the solution on the number line.
a.
x  4 1  3
b.
2x 1  3  6
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Inequalities and Absolute Value
Unit 3
18. Write an absolute value inequality that represents the graph on the number line below.
19. Suppose you start with at least $52 in your savings account and deposit $27 each week. Write an inequality to
describe how much money m you have after w weeks. If you do this for 11 weeks, will you have enough to buy
a bicycle that costs $340? Show your work.
20. Alexandria wants to go hiking on Saturday. She will choose from several parks considering these conditions.
 She wants to hike for 2 hours.
 She wants to spend no more than 6 hours away from home.
 She can average 65 miles per hour to and from the park.
Write and solve an inequality to find possible distances from Alexandria’s home to a park that satisfies the
conditions.
Multiple Choice Questions: Circle the best answer.
21. Students’ scores on an Algebra exam ranged from 60 to 100 . Let e be the exam scores of the students.
Which absolute value inequality represents all of the possible values of e?
A.
e  80  20
B.
e  80  20
C.
e  20  80
D.
e  20  80
B.
x  16
D.
x  16
22. What are the values of x when
A.
C.
x
 6  2?
4
x  32
x 1
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Algebra I Practice Test
23. What is the solution set of
Inequalities and Absolute Value
8 x  3  13?
A.
5

 2, 
4

B.
5

2,  
4

C.
2
D.
5
 
4
24. Which graph represents the solution set for
2 x  4  8 and x  5  7?
A.
B.
C.
D.
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